Universities and other research institutions are increasingly providing additional training in research integrity to improve the quality and reliability of research. Various training courses have been developed, with diverse learning goals and content. Despite the importance of training that focuses on moral character and professional virtues, there remains a lack of training that adopts a virtue ethics approach. To address this, we, a European Commission-funded consortium, have designed a train-the-trainer programme for research integrity. The programme is based on (1) virtue ethics, (2) the ethos of science, (3) learning by doing and (4) learner-centred teaching. The blended learning programme combines e-learning modules with participatory group sessions. Trainers are taught how to guide researchers through a series of structured exercises for fostering reflection on scientific virtues, and how to promote understanding and application of the European Code of Conduct for Research Integrity. Trainers are provided with adaptable tools and resources that can be used and combined in different ways. The programme implementation began in Spring 2020 and 470 trainers have participated to date. When trainers were asked to grade -- between 0 (very bad) and 10 (excellent) -- the e-learning modules and the participatory exercises, 60% scored a grade 8 or higher (median = 8, IQR = 2) for the e-learning modules, whereas 80% scored a grade 8 or higher (median = 9, IQR = 1) for the participatory exercises. A majority felt that the training helped them as a trainer to learn about ways to organise and teach a research integrity course (82%) and would recommend the interactive exercises to others (92%). Trainers have educated over 3300 researchers in Europe using our virtue-based approach. The VIRT[superscript 2]UE train-the-trainer programme fosters research integrity by providing trainers with exercises and tools which enable them to stimulate the development of "good" researchers across Europe.